1. Technical Field
The present invention relates to a flexural vibration element which vibrates in a flexural vibration mode, and various electronic components including the flexural vibration element, such as a vibrator, a resonator, an oscillator gyro, and various sensors.
2. Related Art
As a piezoelectric vibration element in a flexural vibration mode, such a tuning fork type piezoelectric vibration element has been widely used that a pair of vibrating arms is extended in parallel from a base part and the vibrating arms vibrate closer to or away from each other in a horizontal direction. Vibration energy loss generated when the vibrating arms perform flexural vibration causes degradation of performances of a vibrator such as increase of a CI value and decrease of a Q value. Therefore, various ways for preventing or reducing the vibration energy loss has been contrived.
JP-A-2002-261575 as a first example and JP-A-2004-260718 as a second example disclose a tuning fork type quartz crystal vibration element in which cuts or cut-grooves having a predetermined depth are formed at both side parts of a base part from which vibrating arms extend. In the quartz crystal vibration element, even in a case where the vibrating arms generate vibration including a vertical component, vibration leak from the base part is suppressed by the cuts or the cut-grooves so as to improve a trapping effect of the vibration energy and prevent variation of CI values among vibration elements.
Not only such the mechanical loss but also vibration energy loss is generated by heat conduction due to temperature difference between a compressive part and an extending part, which receives tensile stress, of the vibrating arms which performs flexural vibration. Decrease of the Q value caused by the heat conduction is called a thermoelastic effect. In order to prevent or suppress the decrease of the Q value due to the thermoelastic effect, Japanese Patent Application No. 63-110151 as a third example proposes a tuning fork type vibrator, in which a groove or a hole is formed on a centerline of a vibrating arm (vibrating beam) having a rectangular section.
The third example describes that the Q value becomes minimum when a relaxation frequency fm is expressed as fm=1/(2πτ) (here, π denotes circle ratio, τ denotes relaxation time) in a vibrator in a flexural vibration mode. This is based on a relational equation of distortion and stress which is known in a case of internal friction, which is generally caused by temperature difference, of a solid substance. A relationship between a Q value and a frequency is generally expressed as a curve F of FIG. 10 (refer to, for example, C. Zener et al., “Internal Friction in Solids III. Experimental Demonstration of Thermoelastic Internal Friction”, Physical Review, Volume 53, pp. 100-101 (January 1938)). Referring to FIG. 10, the Q value becomes a minimum value Q0 at a relaxation frequency f0 (=1/(2πτ)).
Here, it is also known that the relaxation frequency f0 can be obtained from the following formula.f0=πk/(2ρCpa2)  (1)Here, π denotes circle ratio, k denotes a thermal conductivity in vibration direction of the vibration part(flexural vibration part), ρ denotes a mass density of the vibration part(flexural vibration part), Cp denotes a heat capacity of the vibration part(flexural vibration part), and a denotes a width of the vibration part(flexural vibration part).
Further, JP-A-53-23588 as a fourth example discloses a quartz crystal vibrator in which a tuning fork type oscillation element having two vibrating arms is formed to be integrated with a holding frame, which surrounds the oscillation element and has a rectangular shape, at a connecting part formed on a base part of the oscillation element. The quartz crystal vibrator having such the structure is sealed by sandwiching the holding frame by planar covers from a top and a bottom. Further, JP-A-56-94813 as a fifth example discloses a tuning fork type piezoelectric vibrator in which a vibrator and a rectangular supporting frame are connected by an elastic member provided on a lateral surface of a base part of the vibrator so as to suppress leak of vibration energy of vibrating arms from the base part to an outside.
On the other hand, as a flexural vibrator other than that of a tuning fork type, JP-A-2006-345519 as a sixth example discloses a resonator in which two parallel vibrating arms are coupled to each other by a connecting part and a central arm is extended between the vibrating arms from the connecting part. The resonator is composed of a single-component vibration element made of quartz crystal. In the resonator, at least one groove is formed on at least one of a front surface and a rear surface of the vibrating arms so as to make an excitation electric field even and regionally-strong, reducing energy consumption and limiting a CI value. Further, the groove of the vibrating arms is extended to the connecting part, at which mechanical stress is maximum, and an electric field is extracted at this region so as to increase a vibration coupling effect of the vibrating arms.
Vibration elements vibrating in the flexural vibration mode include a vibration element of an electrostatic driving type using electrostatic force and a vibration element of a magnetic driving type using magnetism as well as the vibration element of the piezoelectric driving type described above. JP-A-5-312576 as a seventh example discloses an angular velocity sensor as a vibration element of the electrostatic driving type. In the angular velocity sensor, a first vibrating body composed of a square frame part is supported by a first supporting beam so as to be able to vibrate in X-axis direction, and a second vibrating body having a square plain plate shape is supported by a second supporting beam so as to be able to vibrate in Y-axis direction, on a substrate made of a silicon material. The first supporting beam bends due to electrostatic force which is generated between a fixed conductive part provided on an end part of the substrate and a movable conductive part provided on an end part of the first vibrating body. Thus the first vibrating body vibrates in the X-axis direction. JP-A-2001-183140 as an eighth example discloses another angular velocity sensor as another vibration element of the electrostatic driving type. This angular velocity sensor is composed of a sensor body made of a silicon wafer and a glass substrate opposed to the sensor body. The sensor body has plummets provided to an inside of a vibration frame, which is supported in a fixed frame by a driving beam, by multiple beams. The sensor body and the plummets vibrate due to electrostatic force generated between parallel plain plate electrodes provided on the sensor body and the glass substrate.
Further, JP-B-43-1194 as a ninth example discloses a vibrating body structure as a vibration element of the magnetic driving type. In the vibrating body structure, a vibrating body made of a constant modulus material is fixed and supported on an external fixing pedestal at its supporting part at one end thereof. A spring part branched from a connecting part between the vibrating body and the pedestal is driven and vibrated by magnet fixed to a free end of the spring part and by an electromagnetic coil fixed to a base. JP-A-10-19577 as a tenth example discloses an angular velocity sensor as another vibration element of the magnetic driving type. In the angular velocity sensor, a thin film magnet is disposed on a thin film vibrating plate which is composed of a silicon substrate and is supported as a cantilever beam. The thin film vibrating plate is vibrated in a thickness direction by an effect of electromagnetic force generated by applying alternating current to a conductor or an electromagnetic coil provided outside the thin film vibrating plate.
The inventor studied a means for suppressing vibration energy loss of vibrating arms in a piezoelectric vibration element having such a structure that one central supporting arm was extended from a connecting part between the two vibrating arms as illustrated in the sixth example. Especially, as far as the inventor knows, almost only the third example studies an influence of the above-mentioned thermoelastic effect given to the piezoelectric vibration element in a flexural vibration mode, among related arts.
FIG. 11A shows a typical example of a piezoelectric vibration element having a related art structure including one central supporting arm. This piezoelectric vibration element 1 includes two vibrating arms 3 and 4 extending from a connecting part 2 in parallel. Between the vibrating arms 3 and 4, one central supporting arm 5 extends in parallel with the arms 3 and 4 at equal distance from the arms 3 and 4. A linear groove 6 is formed on each of a front surface and a rear surface of the vibrating arm 3 and a linear groove 7 is formed on each of a front surface and a rear surface of the vibrating arm 4. The piezoelectric vibration element 1 is fixed and held on a mount part 8 of a package or the like, which is not shown, at an end part 5a, which is opposite to an end at the connecting part, of the central supporting arm 5. When a predetermined voltage is applied to an excitation electrode, which is not shown, in this state, the vibrating arms 3 and 4 perform flexural vibration in a direction closer to or away from each other as shown by arrows in the drawing.
Because of this flexural vibration, mechanical-compressive/-tensile distortion occurred at the central supporting arm 5 in a longitudinal direction of the arm 5. The distortion was observed as temperature-increase and temperature-decrease occurring in the central supporting arm 5. As shown in FIG. 11B, when the vibrating arms 3 and 4 bend in a direction away from each other, the whole of the connecting part 2 bends toward the end part 5a of the central supporting arm 5. Therefore, the central supporting arm 5 receives stress compressing the arm 5 toward the end part 5a. In an opposite manner, when the vibrating arms 3 and 4 bend in a direction coming closer to each other, the connecting part 2 bends toward an opposite side of the end part 5a of the central supporting arm 5 as shown in FIG. 11C. Therefore, the central supporting arm 5 receives stress pulling the arm 5 toward the opposite side of the end part 5a. 
As a result, part of the flexural vibration of the vibrating arms 3 and 4 goes off from the central supporting arm 5 to the mount part 8, that is, mechanical vibration leak occurs, causing increase of a CI value and decrease of a Q value. Thus performance of a vibrator may be degraded. Further, compressive/tensile stress acting on the central supporting arm 5 generates temperature gradient inside the piezoelectric vibration element 1. As a result, vibration energy loss due to the thermoelastic loss may be generated.